An introduction on the multivariate normal-ratio distribution

Sheng Yang, Zhengtao Gui

Published 2023-10-22Version 1

The distribution of the ratio of two random variables which follow the normal distribution has been studied. It gives several representations of the distribution function in terms of the vivariate normal distribution and Nicholson's V function, both of which have been extensively studied. The purpose of this paper is to extend these results to the multivariate case and derive its distribution function. We call this distribution multivariate normal-ratio distribution.